The value of 2$^3$ x a$^3$ x 5a$^4$ will be

Question

Accepted Answer

To determine why Option 3 is the correct answer for the expression $2^3 \times a^3 \times 5a^4$, let's break down the expression step by step:

1. **Evaluate $2^3$:**
   - $2^3$ means $2 \times 2 \times 2$, which equals 8.

2. **Combine the terms involving 'a':**
   - We have $a^3$ and $5a^4$.
   - When multiplying terms with the same base, we add the exponents: $a^3 \times a^4 = a^{3+4} = a^7$.
   - Therefore, $5a^4$ becomes $5 \times a^4$, and when combined with $a^3$, it results in $5a^7$.

3. **Combine all parts of the expression:**
   - Now, we multiply the numerical coefficient 8 (from $2^3$) with the result from the previous step: $8 \times 5a^7$.
   - This simplifies to $40a^7$.

Thus, the expression $2^3 \times a^3 \times 5a^4$ simplifies to $40a^7$.

**Explanation for why Option 3 is correct:**
- Option 3 correctly represents the simplified form of the expression as $40a^7$.

**Explanation for why other options are incorrect:**
- Without the specific details of what Options 1, 2, and 4 are, we can infer that they do not correctly simplify the expression to $40a^7$. They might either have incorrect coefficients, incorrect exponents, or both, which do not match the correct simplification process outlined above.

In conclusion, Option 3 is the correct answer because it accurately reflects the result of simplifying the given expression using the rules of exponents and multiplication.